More immediately next to the venue, Zülpicher Straße and Berrenrather offer a good selection of cafés and food spots for a quick snack.
Closely located to the east of the university is the Belgian Quarter. It is a lively neighborhood known for its vibrant food and drink scene. The area has plenty of cafés, international restaurants, and artisan bakeries. Many of them are located on Aachener Straße or are in close proximity to Brüsseler Platz.
A bit south of the university area, the Südstadt neighborhood offers an inviting mix of traditional and modern eateries. One of the main streets in this particular area is Bonner Straße and all the smaller streets starting from Chlodwigplatz such as Merowingerstraße are worth a look.
To the north-west, Ehrenfeld is yet another scene offering much variety ranging from Turkish street food to modern fusion, all along the Venloer Straße.
If you're particularly keen on places that serve traditional German food, you'll find a large concentration of them downtown, in the Altstadt area. Here's a list of more specific suggestions: Oma Kleinmann, Haus Töller, Max Stark, Brauhaus Päffgen, Brauhaus Sion, Lommerzheim, Brauhaus Früh am Dom, Schreckenskammer, Bier-Esel. But keep in mind that they are rather popular among both tourists and locals, and therefore you might want to book in advance. A selection of typical dishes you might want to try are: "Himmel & Ääd", "Halver Hahn", "Reibekuchen", "Schnitzel", "Rheinischer Sauerbraten" and, of course, Kölsch (the local beer).